#include <itkFEMSolverCrankNicolson.h>

Inheritance diagram for itk::fem::SolverCrankNicolson< TDimension >:

Collaboration diagram for itk::fem::SolverCrankNicolson< TDimension >:

Detailed Description

template<unsigned int TDimension = 3>
class itk::fem::SolverCrankNicolson< TDimension >

FEM Solver for time dependent problems; uses Crank-Nicolson implicit discretization scheme.

This is the main class used for solving FEM time-dependent problems. It solves the following problem:

$( M + \alpha*dt* K )*U_t=(M - (1.- \alpha)*dt* K)* U_{t-1} + dt*(\alpha*f_{n+1} + (1-\alpha)*f_n)$

which is the Crank-Nicolson formulation of the static problem if $\alpha=0.5$ . The static solution is gained if : $\rho = 0.0$ ; $\alpha = 1.0$ ; $dt = 1.0$ ; Practically, it is good to set rho to something small (for the itpack solver). The advantage of choosing $\alpha=0.5$ is that the solution is then stable for any choice of time step, dt. This class inherits and uses most of the Solver class functionality.

Updated: The calls to to AssembleKandM (or AssembleK) and AssembleFforTimeStep (or AssembleF) are now handled internally by calling Update().

FIXME: 1) We should also account for the contribution to the force from essential BCs. Basically there are terms involving $M * (\dot g_b)$ and $ K * g_b $ where $ g_b$ is the essential BC vector.

Definition at line 72 of file itkFEMSolverCrankNicolson.h.

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef Element::Float	Float

typedef SmartPointer< Self >	Pointer

typedef SolverCrankNicolson	Self

typedef Solver< TDimension >	Superclass

Public Types inherited from itk::fem::Solver< TDimension >
typedef SmartPointer< const Self >	ConstPointer

typedef DataObject::Pointer	DataObjectPointer

typedef Element::ArrayType	ElementArray

typedef FEMObjectType::ConstPointer	FEMObjectConstPointer

typedef FEMObjectType::Pointer	FEMObjectPointer

typedef itk::fem::FEMObject < VDimension >	FEMObjectType

typedef Element::Float	Float

typedef InterpolationGridType::DirectionType	InterpolationGridDirectionType

typedef InterpolationGridType::IndexType	InterpolationGridIndexType

typedef InterpolationGridType::Pointer	InterpolationGridPointerType

typedef InterpolationGridType::PointType	InterpolationGridPointType

typedef InterpolationGridType::RegionType	InterpolationGridRegionType

typedef InterpolationGridType::SizeType	InterpolationGridSizeType

typedef InterpolationGridType::SpacingType	InterpolationGridSpacingType

typedef itk::Image < Element::ConstPointer, VDimension >	InterpolationGridType

typedef Load::ArrayType	LoadArray

typedef Material::ArrayType	MaterialArray

typedef Element::Node::ArrayType	NodeArray

typedef SmartPointer< Self >	Pointer

typedef Solver	Self

typedef ProcessObject	Superclass

typedef Element::VectorType	VectorType

typedef ProcessObject::DataObjectPointerArraySizeType	DataObjectPointerArraySizeType

Public Types inherited from itk::ProcessObject
typedef SmartPointer< const Self >	ConstPointer

typedef DataObject::DataObjectIdentifierType	DataObjectIdentifierType

typedef DataObject::Pointer	DataObjectPointer

typedef std::vector < DataObjectPointer >	DataObjectPointerArray

typedef DataObjectPointerArray::size_type	DataObjectPointerArraySizeType

typedef std::vector < DataObjectIdentifierType >	NameArray

typedef SmartPointer< Self >	Pointer

typedef ProcessObject	Self

typedef Object	Superclass

Public Types inherited from itk::Object
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef Object	Self

typedef LightObject	Superclass

Public Types inherited from itk::LightObject
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef LightObject	Self

Public Member Functions
void	AddToDisplacements (Float optimum=1.0)

void	AverageLastTwoDisplacements (Float t=0.5)

Float	BrentsMethod (Float tol=0.01, unsigned int MaxIters=25)

Float	EvaluateResidual (Float t=1.0)

void	FindBracketingTriplet (Float a, Float b, Float *c)

Float	GetCurrentMaxSolution ()

Float	GetDeformationEnergy (Float t=1.0)

LinearSystemWrapper *	GetLS ()

virtual Float	GetTimeStep (void) const

Float	GoldenSection (Float tol=0.01, unsigned int MaxIters=25)

Float	GSMax (Float a, Float b)

Float	GSSign (Float a, Float b)

	itkGetConstMacro (Iterations, unsigned int)

	itkGetMacro (TotalSolutionIndex, unsigned int)

	itkGetMacro (SolutionTMinus1Index, unsigned int)

	itkNewMacro (Self)

	itkTypeMacro (SolverCrankNicolson, Solver< TDimension >)

void	PrintDisplacements ()

void	PrintForce ()

void	PrintMinMaxOfSolution ()

void	RecomputeForceVector (unsigned int index)

void	ResetIterations (void)

void	SetEnergyToMin (Float xmin)

virtual void	SetTimeStep (Float dt)

void	ZeroVector (int which=0)


	itkSetMacro (UseMassMatrix, bool)

	itkGetMacro (UseMassMatrix, bool)


	itkSetMacro (Alpha, Float)

	itkGetMacro (Alpha, Float)


	itkSetMacro (Rho, Float)

	itkGetMacro (Rho, Float)

Public Member Functions inherited from itk::fem::Solver< TDimension >
virtual ::itk::LightObject::Pointer	CreateAnother (void) const

Float	GetDeformationEnergy (unsigned int SolutionIndex=0)

virtual InterpolationGridDirectionType	GetDirection ()

const Element *	GetElementAtPoint (const VectorType &pt) const

FEMObjectType *	GetInput (void)

FEMObjectType *	GetInput (unsigned int idx)

LinearSystemWrapper::Pointer	GetLinearSystemWrapper ()

virtual const char *	GetNameOfClass () const

virtual InterpolationGridPointType	GetOrigin ()

virtual InterpolationGridRegionType	GetRegion ()

Float	GetSolution (unsigned int i, unsigned int which=0)

virtual InterpolationGridSpacingType	GetSpacing ()

void	InitializeInterpolationGrid (const InterpolationGridSizeType &size, const InterpolationGridPointType &bb1, const InterpolationGridPointType &bb2)

virtual void	SetDirection (InterpolationGridDirectionType _arg)

virtual void	SetInput (FEMObjectType *fem)

virtual void	SetInput (unsigned int, FEMObjectType *fem)

void	SetLinearSystemWrapper (LinearSystemWrapper::Pointer ls)

virtual void	SetOrigin (InterpolationGridPointType _arg)

virtual void	SetRegion (InterpolationGridRegionType _arg)

virtual void	SetSpacing (InterpolationGridSpacingType _arg)

void	InitializeInterpolationGrid (const InterpolationGridSizeType &size)

void	InitializeInterpolationGrid (const InterpolationGridRegionType &region, const InterpolationGridPointType &origin, const InterpolationGridSpacingType &spacing, const InterpolationGridDirectionType &direction)

const InterpolationGridType *	GetInterpolationGrid (void) const

virtual DataObjectPointer	MakeOutput (DataObjectPointerArraySizeType)

FEMObjectType *	GetOutput (void)

FEMObjectType *	GetOutput (unsigned int idx)

Public Member Functions inherited from itk::ProcessObject
virtual void	AbortGenerateDataOff ()

virtual void	AbortGenerateDataOn ()

virtual void	EnlargeOutputRequestedRegion (DataObject *)

virtual const bool &	GetAbortGenerateData ()

NameArray	GetInputNames () const

MultiThreader *	GetMultiThreader () const

DataObjectPointerArraySizeType	GetNumberOfIndexedInputs () const

DataObjectPointerArraySizeType	GetNumberOfInputs () const

DataObjectPointerArraySizeType	GetNumberOfOutputs () const

virtual DataObjectPointerArraySizeType	GetNumberOfValidRequiredInputs () const

NameArray	GetOutputNames () const

virtual const float &	GetProgress ()

NameArray	GetRequiredInputNames () const

bool	HasInput (const DataObjectIdentifierType &key) const

bool	HasOutput (const DataObjectIdentifierType &key) const

virtual DataObjectPointer	MakeOutput (const DataObjectIdentifierType &)

virtual void	PrepareOutputs ()

virtual void	PropagateRequestedRegion (DataObject *output)

virtual void	ResetPipeline ()

virtual void	SetAbortGenerateData (bool _arg)

virtual void	SetProgress (float _arg)

virtual void	Update ()

virtual void	UpdateLargestPossibleRegion ()

virtual void	UpdateOutputData (DataObject *output)

virtual void	UpdateOutputInformation ()

void	UpdateProgress (float amount)

DataObjectPointerArray	GetInputs ()

DataObjectPointerArray	GetOutputs ()

DataObjectPointerArray	GetIndexedInputs ()

DataObjectPointerArray	GetIndexedOutputs ()

DataObjectPointerArraySizeType	GetNumberOfIndexedOutputs () const

virtual void	SetReleaseDataFlag (bool flag)

virtual bool	GetReleaseDataFlag () const

void	ReleaseDataFlagOn ()

void	ReleaseDataFlagOff ()

virtual void	SetReleaseDataBeforeUpdateFlag (bool _arg)

virtual const bool &	GetReleaseDataBeforeUpdateFlag ()

virtual void	ReleaseDataBeforeUpdateFlagOn ()

virtual void	ReleaseDataBeforeUpdateFlagOff ()

virtual void	SetNumberOfThreads (ThreadIdType _arg)

virtual const ThreadIdType &	GetNumberOfThreads ()

Public Member Functions inherited from itk::Object
unsigned long	AddObserver (const EventObject &event, Command *)

unsigned long	AddObserver (const EventObject &event, Command *) const

virtual void	DebugOff () const

virtual void	DebugOn () const

Command *	GetCommand (unsigned long tag)

bool	GetDebug () const

MetaDataDictionary &	GetMetaDataDictionary (void)

const MetaDataDictionary &	GetMetaDataDictionary (void) const

virtual ModifiedTimeType	GetMTime () const

virtual const TimeStamp &	GetTimeStamp () const

bool	HasObserver (const EventObject &event) const

void	InvokeEvent (const EventObject &)

void	InvokeEvent (const EventObject &) const

virtual void	Modified () const

virtual void	Register () const

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag)

void	SetDebug (bool debugFlag) const

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

virtual void	SetReferenceCount (int)

virtual void	UnRegister () const

Public Member Functions inherited from itk::LightObject
virtual void	Delete ()

virtual int	GetReferenceCount () const

	itkCloneMacro (Self)

void	Print (std::ostream &os, Indent indent=0) const

Protected Member Functions
void	AssembleFforTimeStep (int dim=0)

void	AssembleKandM ()

void	GenerateData ()

void	InitializeForSolution ()

virtual void	RunSolver (void)

	SolverCrankNicolson ()

	~SolverCrankNicolson ()

Protected Member Functions inherited from itk::fem::Solver< TDimension >
	Solver ()

virtual	~Solver ()

void	PrintSelf (std::ostream &os, Indent indent) const

void	GenerateData ()

void	AssembleK ()

virtual void	InitializeMatrixForAssembly (unsigned int N)

virtual void	FinalizeMatrixAfterAssembly (void)

virtual void	AssembleElementMatrix (Element::Pointer e)

virtual void	AssembleLandmarkContribution (Element::ConstPointer e, float)

void	ApplyBC (int dim=0, unsigned int matrix=0)

void	AssembleF (int dim=0)

void	DecomposeK (void)

void	UpdateDisplacements (void)

void	FillInterpolationGrid (void)

virtual void	InitializeLinearSystemWrapper (void)

Protected Attributes
Float	m_Alpha

Float	m_CurrentMaxSolution

unsigned int	m_DifferenceMatrixIndex

unsigned int	m_DiffMatrixBySolutionTMinus1Index

unsigned int	m_ForceTIndex

unsigned int	m_ForceTMinus1Index

unsigned int	m_ForceTotalIndex

unsigned int	m_Iterations

Float	m_Rho

unsigned int	m_SolutionTIndex

unsigned int	m_SolutionTMinus1Index

unsigned int	m_SolutionVectorTMinus1Index

unsigned int	m_SumMatrixIndex

Float	m_TimeStep

unsigned int	m_TotalSolutionIndex

bool	m_UseMassMatrix

Protected Attributes inherited from itk::fem::Solver< TDimension >
unsigned int	m_NGFN

unsigned int	m_NMFC

LinearSystemWrapper::Pointer	m_ls

LinearSystemWrapperVNL	m_lsVNL

InterpolationGridPointerType	m_InterpolationGrid

FEMObjectPointer	m_FEMObject

Private Member Functions
void	operator= (const Self &)

	SolverCrankNicolson (const Self &)

Additional Inherited Members
Static Public Member Functions inherited from itk::fem::Solver< TDimension >
static Pointer	New ()

Static Public Attributes inherited from itk::fem::Solver< TDimension >
static const unsigned int	FEMDimension

static const unsigned int	MaxDimensions

Protected Types inherited from itk::LightObject
typedef int	InternalReferenceCountType

Member Typedef Documentation

template<unsigned int TDimension = 3>

typedef SmartPointer<const Self> itk::fem::SolverCrankNicolson< TDimension >::ConstPointer

Definition at line 78 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

typedef Element::Float itk::fem::SolverCrankNicolson< TDimension >::Float

Definition at line 86 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

typedef SmartPointer<Self> itk::fem::SolverCrankNicolson< TDimension >::Pointer

Definition at line 77 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

typedef SolverCrankNicolson itk::fem::SolverCrankNicolson< TDimension >::Self

Definition at line 75 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

typedef Solver<TDimension> itk::fem::SolverCrankNicolson< TDimension >::Superclass

Definition at line 76 of file itkFEMSolverCrankNicolson.h.

Constructor & Destructor Documentation

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::SolverCrankNicolson ( )

protected

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::~SolverCrankNicolson ( )

inlineprotected

Definition at line 207 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::SolverCrankNicolson ( const Self & )

private

Member Function Documentation

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::AddToDisplacements ( Float optimum = 1.0 )

Add solution vector u to the corresponding nodal values, which are stored in node objects). This is standard post processing of the solution

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::AssembleFforTimeStep ( int dim = 0 )

protected

Assemble the master force vector at a given time.

Parameters

dim	This is a parameter that can be passed to the function and is normally used with isotropic elements to specify the dimension for which the master force vector should be assembled.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::AssembleKandM ( )

protected

Assemble the master stiffness and mass matrix. We actually assemble the right hand side and left hand side of the implicit scheme equation.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::AverageLastTwoDisplacements ( Float t = 0.5 )

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::BrentsMethod	(	Float	tol = `0.01`,
		unsigned int	MaxIters = `25`
	)

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::EvaluateResidual ( Float t = 1.0 )

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::FindBracketingTriplet	(	Float *	a,
		Float *	b,
		Float *	c
	)

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::GenerateData ( )

protectedvirtual

Method invoked by the pipeline in order to trigger the computation of the registration.

Reimplemented from itk::ProcessObject.

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::GetCurrentMaxSolution ( )

inline

Definition at line 195 of file itkFEMSolverCrankNicolson.h.

References itk::fem::SolverCrankNicolson< TDimension >::m_CurrentMaxSolution.

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::GetDeformationEnergy ( Float t = 1.0 )

template<unsigned int TDimension = 3>

LinearSystemWrapper* itk::fem::SolverCrankNicolson< TDimension >::GetLS ( )

inline

Definition at line 190 of file itkFEMSolverCrankNicolson.h.

References itk::fem::Solver< TDimension >::m_ls.

template<unsigned int TDimension = 3>

virtual Float itk::fem::SolverCrankNicolson< TDimension >::GetTimeStep ( void ) const

inlinevirtual

Returns the time step used for dynamic problems.

Reimplemented from itk::fem::Solver< TDimension >.

Definition at line 142 of file itkFEMSolverCrankNicolson.h.

References itk::fem::SolverCrankNicolson< TDimension >::m_TimeStep.

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::GoldenSection	(	Float	tol = `0.01`,
		unsigned int	MaxIters = `25`
	)

Finds the optimum value between the last two solutions and sets the current solution to that value. Uses Evaluate Residual;

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::GSMax	(	Float	a,
		Float	b
	)

inline

Definition at line 183 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

Float itk::fem::SolverCrankNicolson< TDimension >::GSSign	(	Float	a,
		Float	b
	)

inline

Definition at line 179 of file itkFEMSolverCrankNicolson.h.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::InitializeForSolution ( )

protected

helper initialization function before assembly but after generate GFN.

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetConstMacro	(	Iterations	,
		unsigned	int
	)

Get the number of iterations run for the solver

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetMacro	(	UseMassMatrix	,
		bool
	)

Get/Set the use of the Mass Matrix for the solution

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetMacro	(	TotalSolutionIndex	,
		unsigned	int
	)

Get the index for the current solution

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetMacro	(	SolutionTMinus1Index	,
		unsigned	int
	)

Get the index for the previous solution

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetMacro	(	Alpha	,
		Float
	)

Set stability step for the solution. Initialized to 0.5

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkGetMacro	(	Rho	,
		Float
	)

Set density constant.

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkNewMacro ( Self )

Method for creation through the object factory.

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkSetMacro	(	UseMassMatrix	,
		bool
	)

Get/Set the use of the Mass Matrix for the solution

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkSetMacro	(	Alpha	,
		Float
	)

Set stability step for the solution. Initialized to 0.5

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkSetMacro	(	Rho	,
		Float
	)

Set density constant.

template<unsigned int TDimension = 3>

itk::fem::SolverCrankNicolson< TDimension >::itkTypeMacro	(	SolverCrankNicolson< TDimension >	,
		Solver< TDimension >
	)

Run-time type information (and related methods)

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::operator= ( const Self & )

private

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::PrintDisplacements ( )

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::PrintForce ( )

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::PrintMinMaxOfSolution ( )

Compute and print the minimum and maximum of the total solution and the last solution.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::RecomputeForceVector ( unsigned int index )

compute the current state of the right hand side and store the current force for the next iteration.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::ResetIterations ( void )

inline

Reset the number of iterations for the solver. This will prompt the Solver to Assemble the master stiffness and mass matrix again. This is only generated before the first iteration.

Definition at line 106 of file itkFEMSolverCrankNicolson.h.

References itk::fem::SolverCrankNicolson< TDimension >::m_Iterations.

template<unsigned int TDimension = 3>

virtual void itk::fem::SolverCrankNicolson< TDimension >::RunSolver ( void )

protectedvirtual

Solve for the displacement vector u at a given time. Update the total solution as well.

Reimplemented from itk::fem::Solver< TDimension >.

template<unsigned int TDimension = 3>

void itk::fem::SolverCrankNicolson< TDimension >::SetEnergyToMin ( Float xmin )